Distributed  array for direction and frequency  finding

ABSTRACT

An optical imaging system and method that reconstructs RF sources in k-space by utilizing interference amongst modulated optical beams. In some examples, the system and method may record the interference pattern produced by RF-modulated optical beams conveyed by optical fibers having unequal lengths. The photodetectors record the interference, and computational analysis using known tomography reconstruction methods is performed to reconstruct the RF sources in k-space.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a Continuation of U.S. application Ser. No.16/430,877 filed Jun. 4, 2019, which is a Continuation of U.S.application Ser. No. 15/956,545 filed Apr. 18, 2018, which is anon-provisional of U.S. Provisional Application 62/486,474 and acontinuation-in-part of U.S. application Ser. No. 15/227,859 filed Aug.3, 2017, which claims the benefit of U.S. Provisional Application No.62/200,626 filed on Aug. 3, 2015, the disclosure of each of theseapplications being hereby incorporated by reference in its entirety.

FIELD OF TECHNOLOGY

The herein described subject matter and associated exemplaryimplementations are directed to improvements, extensions and variationsof an imaging receiver as described in U.S. Pat. No. 7,965,435 and U.S.Patent Publication No. 2016/0006516, the disclosures of each beinghereby incorporated by reference in their entireties.

BACKGROUND

Many existing antenna-array-based receivers are unable to detect bothlocation and frequency of an incoming RF signal without significantfiltering or other processing. In such systems, the received broadbandradiation is divided into multiple narrow-band channels that areprocessed individually to determine the information content, and,potentially, the angle of arrival (AoA) of the received radiation. Suchprocessing requires banks of high-speed receivers to sift through thevast amount of data in search of signals of interest. Imaging receiversmay rely on distributed aperture to sample incoming electromagneticradiation, which is then up-converted to optical domain for conveyanceand processing. The up-conversion process preserves the phase andamplitude information of radio frequency (RF) waves in the opticaldomain, which thereby allows optical reconstruction of the RF scene.However, the optical reconstruction in imaging receivers (the spatiallocation of the optical signals on the image sensor) is dependent on thefrequency of the RF waves. Thus, when there are sources of different RFfrequency being processed simultaneously, their locations in the realworld could not be previously unambiguously identified by imagingreceivers. Other types of receivers have similar deficiencies.

SUMMARY

The herein described exemplary implementations provide novel approachesto extracting information about radio frequency (RF) emitters fromreceived electromagnetic radiation, such as electromagnetic radiationranging between 100 MHz and 300 GHz. The exemplary implementations mayprovide real-time, simultaneous determination of carrier frequency,amplitude and angle of arrival (AoA) of multiple RF sources in an RFscene. In some exemplary embodiments, instantaneous bandwidth (IBW) mayapproach 100 GHz. This capability may be achieved without sacrifice ofsignal-to-noise ratio (SNR), by virtue of an antenna array whose gainmore than compensates for the added thermal noise that accompanies suchwide IBW. The optical and RF approaches described herein may enable thearray's entire field of regard (i.e. its full beam steering range) to becontinuously detected and processed in real time.

One exemplary implementation of a receiver includes a phased arrayantenna having a plurality of antenna elements arranged in a firstpattern configured to receive RF signals from at least one RF source. Aplurality of RF waveguides each transmit RF signals from each of theantenna elements to an RF coupler with a different time delay betweenthe antenna element and the RF coupler. The RF coupler allows the RFsignals to interfere with each other, and has an output interferencepattern comprising a plurality of RF interference signals. Theinterference pattern is detected and used to computationally reconstructRF sources in k-space.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1A is an illustration of an RF receiver, according to certainexemplary embodiments;

FIG. 1B is another illustration of an RF receiver in accordance withaspects of the invention, according to certain exemplary embodiments;

FIGS. 2A, 2B and 2C are block diagrams of components for use with the RFreceiver of FIG. 1A or 1B, according to certain exemplary embodiments;

FIG. 2D illustrates details of an embodiment where the detector maycapture in real-time an image of a selected frequency of an RF scene,according to certain exemplary embodiments;

FIGS. 3A, 3B and 3C are schematic drawings illustrating various RF planewaves detected by the imaging receiver of FIG. 1, according to certainexemplary embodiments;

FIG. 4 is a schematic drawing illustrating k-space representation of theimaging receiver, according to certain exemplary embodiments;

FIG. 5 is a schematic drawing illustrating of a generalized imagingreceiver, according to certain exemplary embodiments;

FIG. 6 is a graphical representation of RF scene reconstruction,according to certain exemplary embodiments;

FIG. 7 depicts the sampling of the spatial-temporal aperture used in thereconstruction of FIG. 6, according to certain exemplary embodiments;

FIG. 8 is a schematic drawing illustrating an imaging receiver arrangedso as to receive off-axis incidence for all received RF radiation,according to certain exemplary embodiments;

FIG. 9 depicts the projection of k-space in the receiver configurationof FIG. 8, according to certain exemplary embodiments;

FIG. 10 is a schematic drawing illustrating a combination of twooff-axis imaging receivers for AoA/frequency disambiguation, accordingto certain exemplary embodiments;

FIG. 11A is a schematic drawing illustrating a visualization of 3Dk-vector space performed by two arrays, according to certain exemplaryembodiments;

FIG. 11B is a schematic drawing illustrating a visualization of 3D realspace performed by visual stereoscopic imaging, according to certainexemplary embodiments;

FIG. 12 is a schematic drawing illustrating a dual array for 3D k-spacereconstruction with interleaved arrays, according to certain exemplaryembodiments;

FIG. 13 depicts k-space representation of stereoscopic imager with twosets of lines of projection, according to certain exemplary embodiments;

FIG. 14 is a schematic drawing illustrating a single array with two RFimaging axes, according to certain exemplary embodiments;

FIG. 15 is a schematic drawing illustrating a dual imaging receiver withshared optical reconstruction system, according to certain exemplaryembodiments;

FIG. 16 is a flowchart of a method performed by an imaging receiver,according to certain exemplary embodiments;

FIGS. 17A-17C illustrate exemplary configurations where RF radiationdetected by antennas are transmitted along RF waveguides to an RFcoupler, according to certain exemplary embodiments;

FIGS. 18A-18C illustrate example RF couplers, according to certainexemplary embodiments;

FIGS. 19A-19F illustrate details of example RF couplers, according tocertain exemplary embodiments;

FIG. 20 illustrates an example of an RF detector for detecting the powerof an RF signal received from a corresponding transmission line of an RFcoupler, according to certain exemplary embodiments; and

FIG. 21 illustrates an example method that may be implemented by RFdomain k-space detectors, according to certain exemplary embodiments.

DETAILED DESCRIPTION

The present disclosure now will be described more fully hereinafter withreference to the accompanying drawings, in which various exemplaryimplementations are shown. The invention may, however, be embodied inmany different forms and should not be construed as limited to theexample exemplary implementations set forth herein. These exampleexemplary implementations are just that—examples—and manyimplementations and variations are possible that do not require thedetails provided herein. It should also be emphasized that thedisclosure provides details of alternative examples, but such listing ofalternatives is not exhaustive. Furthermore, any consistency of detailbetween various examples should not be interpreted as requiring suchdetail—it is impracticable to list every possible variation for everyfeature described herein. The language of the claims should bereferenced in determining the requirements of the invention.

Although the figures described herein may be referred to using languagesuch as “one exemplary implementations,” or “certain exemplaryimplementations,” these figures, and their corresponding descriptionsare not intended to be mutually exclusive from other figures ordescriptions, unless the context so indicates. Therefore, certainaspects from certain figures may be the same as certain features inother figures, and/or certain figures may be different representationsor different portions of a particular exemplary implementation.

The terminology used herein is for the purpose of describing particularexemplary implementations only and is not intended to be limiting of theinvention. As used herein, the singular forms “a”, “an” and “the” areintended to include the plural forms as well, unless the context clearlyindicates otherwise. As used herein, the term “and/or” includes any andall combinations of one or more of the associated listed items and maybe abbreviated as “/”.

It will be understood that the terms “comprises” and/or “comprising,” or“includes” and/or “including” when used in this specification, specifythe presence of stated features, regions, integers, steps, operations,elements, and/or components, but do not preclude the presence oraddition of one or more other features, regions, integers, steps,operations, elements, components, and/or groups thereof.

It will be further understood that when an element is referred to asbeing “connected” or “coupled” to or “on” another element, it can bedirectly connected or coupled to or on the other element or interveningelements may be present. In contrast, when an element is referred to asbeing “directly connected” or “directly coupled” to another element, oras “contacting” or “in contact with” another element, there are nointervening elements present. Other words used to describe therelationship between elements should be interpreted in a like fashion(e.g., “between). Unless otherwise defined, all terms (includingtechnical and scientific terms) used herein have the same meaning ascommonly understood by one of ordinary skill in the art to which thisdisclosure belongs. It will be further understood that terms, such asthose defined in commonly used dictionaries, should be interpreted ashaving a meaning that is consistent with their meaning in the context ofthe relevant art and/or the present application, and will not beinterpreted in an idealized or overly formal sense unless expressly sodefined herein.

As is traditional in the field of the disclosed technology, features andexemplary implementations are described, and illustrated in thedrawings, in terms of functional blocks, units and/or modules. Thoseskilled in the art will appreciate that these blocks, units and/ormodules are physically implemented by electronic (or optical) circuitssuch as logic circuits, discrete components, microprocessors, hard-wiredcircuits, memory elements, wiring connections, and the like, which maybe formed using semiconductor-based fabrication techniques or othermanufacturing technologies. In the case of the blocks, units and/ormodules being implemented by microprocessors or similar, they may beprogrammed using software (e.g., microcode) to perform various functionsdiscussed herein and may optionally be driven by firmware and/orsoftware. Alternatively, each block, unit and/or module may beimplemented by dedicated hardware, or as a combination of dedicatedhardware to perform some functions and a processor (e.g., one or moreprogrammed microprocessors and associated circuitry) to perform otherfunctions. Also, each block, unit and/or module of the exemplaryimplementations may be physically separated into two or more interactingand discrete blocks, units and/or modules without departing from thescope of the inventive concepts. Further, the blocks, units and/ormodules of the exemplary implementations may be physically combined intomore complex blocks, units and/or modules without departing from thescope of the inventive concepts.

Aspects of the disclosure are related to devices and associated methodsfor improving a wideband radio-frequency (RF) phased-array receiver. Theembodiments described here may determine a signal's angle of arrival(AoA) and frequency in real time. Aspects of the embodiments provide asignal detection mechanism wherein RF signals are upconverted byfiber-coupled electro-optic modulators driven by the antenna elements ofa phased array. The conversion results in sidebands on an opticalcarrier wave supplied by a laser. These optical sidebands aresubstantially proportional in power to the RF power incident into eachantenna element, and also preserve the phase carried by the incident RFsignal. This RF upconversion allows the optical sidebands to be used toreconstruct an image of the RF energy in the scene.

An imaging receiver 100 in accordance with aspects of the invention isdepicted in FIGS. 1A and 1B wherein similar or like elements areidentified by the same reference numerals. The illustrated imagingreceiver 100 is a phased-array receiver. The imaging receiver 100includes a processor 200 coupled to the various components within thereceiver to implement the functionality described herein. The processormay be a general purpose processor (e.g., part of a general purposecomputer, such as a PC) or dedicated processor (e.g., digital signalprocessor (DSP), FPGA (field programmable gate array)). The processormay be configured with software to control the component of the imagingreceiver 100. Variations of suitable processors for use in the imagingreceiver 100 will be understood by one of skill in the art from thedescription herein.

A phased-array antenna 110, e.g., a sparse array of M antenna elements120 arranged in a first pattern as shown in the example of FIG. 1B,receives RF signals from an external source. Various patterns of thearrangement of the M antenna elements 120 are described further herein,and may include planar arrangements, conformal arrangements conformingto a non-planar three dimensional surface (e.g., a surface of a vehicle,such as the hull of an airplane or helicopter), regularly spacedarrangements (e.g., regularly spaced in a two dimensional array) or anirregularly spaced array. While the antenna elements 120 shown in FIGS.1A and 1B are horn antennae, those of skill in the art will understandthat a variety of antenna means may be used. RF signals sampled at theantenna elements 120 are used to modulate a laser beam split M ways. Anelectro-optic (EO) modulator 130 is coupled to each of the antennaelements 120 and receives a branch of the split laser beam that it usesto convert the RF energy received at each antenna element 120 to theoptical domain. It does so by modulating the optical (carrier) beamproduced by the laser 125 (FIGS. 1A, 1B, 2A). The time-variantmodulation manifests itself in the frequency domain as a set ofsidebands flanking the original carrier frequency (or wavelength), atwhich the source laser operates, as illustrated in FIG. 2B, which isdiscussed in more detail below. As a result, the energy radiated in theRF domain appears in the optical domain as sidebands of the carrierfrequency. This up-conversion of the RF signal into optical domain maybe coherent so that all the phase and amplitude information present inRF is preserved in the optical sidebands. This property of coherencepreservation in optical up-conversion allows the recovery of theRF-signal angle of arrival using optical means.

As shown in FIG. 1B, the modulated optical beams containing the lasercarrier wavelength and the sidebands with imprinted RF signal areconveyed by optical fibers 140 to a lenslet array 150 (FIG. 1B) coupledto the outputs 141 of the fibers 140 that are arranged in a secondpattern. The second pattern may or may not mimic or correspond to thefirst pattern of the array of the RF antennas at a reduced scale.

FIG. 2C illustrates the output ends of the optical fibers 140 arrangedin a pattern which may correspond to the pattern of the antenna elements120 of FIG. 1. From the outputs 141 of the optical fibers 140 at thelenslet array 150 on, the beams propagate in free space, no longerguided by the optical fibers, and form a combined beam 160 where thelight emanating from fiber outputs interfere. While this embodimentshows conventional optical fibers 140 between the electro-opticmodulators 130 and the lenslet array 150, those of skill in the art willappreciate that other optical waveguides or channels may also or insteadbe used. Similarly, while this embodiment illustrates the use of a freespace as a channel for forming a composite optical beams 160 and 185from light emanating from the outputs of the optical fibers 140, thoseskilled in the art will appreciate that other optical channels can beused for forming a composite optical beam 160 and/or 185.

As shown in FIG. 1B, the individual beams propagate in free space fromthe outputs 141 of fibers 140 at the lenslet array 150, which allows theindividual beams to interfere with one-another where they overlap toform the combined or composite beam 160. Part of the optical compositebeam 160 is split off with a beam-splitter 165, mixed with a referencebeam 170, and sent to an array of detectors 175 (phase-compensationdetectors) in order to detect, and, if desired, allow for thecompensation of, optical phase variation originating in the individualfibers 140 due to environmental conditions such as vibrations andacoustics. An optional band-pass optical filter 180, may strip off thecarrier wavelength and allow only one of the sidebands through (see FIG.2B). The resulting overlapping beams forming a composite beam projectedonto photodetector 190, e.g., an image sensor array formed on asemiconductor chip, such as a charge coupled device (CCD) array, CMOSimage sensor array, and/or a photodiode array, an optical camera, and/orother standard image sensors. Thus, the overlapping beams form compositebeam 185 where they interfere to form a representation of the RF signalin the optical domain.

As shown in FIG. 1A, the free space optics may include optical filteringand interference module 192 and photodetector array 190 which allows thebeams emanating from the outputs of fibers 140 to interfere with eachother in free space prior to detection and recordation by photodetectorarray 190.

FIG. 2B illustrates the use of an optical filter 180 to recover orisolate an optical sideband that corresponds to a received RF signal,which may for example be a millimeter wave (MMW) signal having afrequency Wm. As shown in the graphs of FIG. 2B, the received RFsignal(s) from antenna element(s) 120 modulate an optical carrier signal(source) 125 operating at a frequency ω₀ (illustratively at a wavelengthbetween 1557 and 1558 nm). The output 135 of modulator 130 includes anoptical analog of the MMW signal in sidebands of the optical carrier asshown in the middle graph. The output 135 of modulator 130 istransmitted via a corresponding optical fiber 140. An optical band-passfilter 180 tuned to ω₀+ω_(m) or ω₀−ω_(m) strips off (isolates) theoptical representation of the received MMW signal(s) from the carrier.

FIG. 2A depicts the configuration of an imaging receiver 100 with anemphasis on the optical layer. The single laser source 125 is split Mways by a splitter 127 and the beams 128 are routed through modulators130 coupled to antennas 120 capturing the RF radiation. The (optical)outputs 135 of the modulators 130 are filtered to allow only a singlesideband corresponding to the captured RF radiation to pass, for exampleusing a filter 180 as described with respect to FIG. 2B. The free-spaceinterference of the optical composite beam 185 output from filter 180among the M different channels yields a pattern measured with detectors190, as discussed in more detail below.

Note that FIGS. 1 and 2A depict the filter 180 positioned in thefree-space portion of the imaging receiver 100 downstream of the lensletarray 150. In some exemplary implementations the filter is optional andis not a necessary component of the system or methodology. In yet otherimplementations, the filter can be placed anywhere between themodulators 130 and the detector 190 to enable reconstruction of theRF-source position in the optical domain. Furthermore, in some exemplaryimplementations, especially for frequencies lower than ˜5 GHz, aMach-Zehnder modulator (MZM) may be used to filter out the sidebandenergy from the optical carrier energy. Such modulators can, underappropriate bias conditions, interferometrically suppress the carrierwhile passing the (odd-order) sidebands, thereby suppressing the carrierin a frequency-independent manner. In yet other implementations, nophysical filter may be used, and the system may rely on thecomputational reconstruction to account for the presence of the opticalcarrier in the interference pattern. In yet other implementations, thephysical arrangement of the optical channels, including the antennas120, the lenslet array 150 and/or the optical fiber lengths, and/or theapplied optical phases by properly biasing modulators 130, or by othermeans, may be so organized as to produce the interference pattern of thecarrier wavelength significantly separated spatially from theinterference pattern produced by the sidebands. Other implementationsmay combine some or all of the approaches listed above.

The detector 190 of FIGS. 1A and 1B may be an array of photo-detectorssuch as those of a charged coupled device (CCD) or contact image sensoror CMOS image sensor, which in some embodiments may not be able toprocess (e.g. decode) information present in the RF signals received bythe antenna array 110 with the same performance as high-speedphotodiodes. In some exemplary implementations, to extract or recoverinformation encoded in the RF signals input by the antenna elements 120,the composite optical beam output from filter 180 is further split withadditional beam-splitters and combined with reference laser beams forheterodyne detection by a high speed photodetector (see, e.g., U.S.Patent Pub. No. 2016/0006516).

Below, further details on the optical capture of the RF scene arepresented. To capture the RF scene in the optical domain, the (optical)outputs of the modulators 130 are carried in optical fibers 140 to alenslet array 150 (FIG. 2C). The arrangement of the optical fibers 140need not mimic the spatial distribution of the corresponding antennas120 to which the optical fibers are attached. For example, a sequence ofoptical fibers along a particular direction may be different than asequence of the corresponding antennas 120 to which they are attached (asequence of these antennas 120 along a particular line or curve, e.g.).The fibers may also be split so as to produce a higher number of opticaloutput beams than the number of antennas 120. However, the arrangementof the optical fibers 140 may also mimic the spatial distribution of theantennas 120 to which they are attached. The output beams are thenallowed to interfere in free space (or other suitable channel or mediumfor forming a composite optical signal), and the interference patterncorresponding to the original RF scene is captured by an array ofoptical sensors such as detector 190 (e.g., a CCD semiconductor chip).Such an interference space may be transparent and may comprise a vacuum,air, a gas other than air, a liquid or a solid (e.g., a lens or a slabwaveguide).

Given that the positions of the individual antenna elements 120 in thearray 110 are fixed, the phase relations of waves sampled by theseelements depend on both the angle of arrival and on the frequency. Forexample, in a system where the geometry of the lenslet array 150 matchesthe geometry of the antenna array 110, two waves arriving at the RFaperture from the same direction but differing in frequency will(normally) reconstruct in the optical domain as bright spots indifferent positions on the image plane (e.g., on photodetector 190 fordetection and processing by processor 200), as shown in FIG. 3A. Theamount of spatial offset between different RF waves with differentfrequencies incident upon the array depends on the incidence angle: forwaves arriving at the array along the RF imaging axis, or achromaticaxis (which may be considered an incidence angle equal to zero), all RFfrequencies reconstruct to a single spot lying on the optical axis ofthe imaging system. The greater the incidence angle of the RF wave withrespect to the RF imaging axis, the greater the spread of the resultingoptical image as a function frequency. Using the terminology from thefield of imaging optics, such spreading of an image due to change infrequency (wavelength) is referred to herein as chromatic aberration.

The effect of chromatic aberration in the imaging receiver withhomothetic arrays 110 and 150 is illustrated in FIG. 3A. It will beappreciated that the optical reconstruction referenced below (e.g.,detection of optical spots) may be performed by an imaging receiver,such as the imaging receiver 100 described herein. The opticalreconstruction may be captured in real time by detector 190 of theimaging receiver 100. For example, the optical dots discussed herein maybe detected by detector 190 and processed by processor 200. For suchoptical reconstruction, the imaging receiver may use a single detector190 detecting light of a single composite beam 185 formed from one ormore optical fiber bundles (where the outputs of the plural opticalbundles described herein are combined), or in certain examples, use asingle antenna array 110 that has outputs of separate optical fiberbundles to different ones of plural detectors 190, where each detector190 is associated with separate optical processing elements describedhere, and each detector 190 is associated with a separate optical fiberbundle. FIG. 3A illustrates incoming RF radiation at frequencies Ω₁ andΩ₂ incident upon the array. The angle of arrival is identical for thetwo RF beams, but the frequencies (wavelengths) differ. Reconstructed inoptical domain, two spatially-separated spots are formed: onecorresponding to incoming frequency Ω₁ and the other to Ω₂.

Chromatic aberration can also be understood with the help of wave-vector(or k-space) description of the image reconstruction. An RF plane waveincident upon the antenna array is represented by a wave vector (ak-vector) pointing in a direction perpendicular to the phase-front andhaving length proportional to the frequency; the k-vector points in thedirection of propagation of the wave. The imaging receiver, by virtue ofupconverting the RF waves to the optical domain followed by opticalreconstruction of the RF waves (e.g., by photodetector 190), may map thek-vectors of the incoming RF waves onto the image plane of the opticallens, see FIG. 3B. The k-vectors corresponding to all possible RF planewaves form a three-dimensional vector space. This 3D space is mappedonto a two-dimensional space: the image plane of the imaging lens, whichmay correspond to the 2D plane of the photodetector 190 when implementedas an image sensor. The 3D to 2D mapping may be a projection along theachromatic axis of the imaging receiver 100. As a result, k-vectorsdiffering by a vector parallel to the achromatic axis of the imagingreceiver 100 are mapped to the same point in the image plane. Thissituation is shown in FIG. 3C where plane waves corresponding to vectorsk₁, k₂, and k₃ are all mapped to a single point in the image plane asthey differ from one another by a vector parallel to the achromaticaxis. In contrast, wave-vectors k₄ and k₅ are mapped to two separatepoints in the image plane even though they are parallel to one another,i.e. they correspond to plane waves coming from the same direction. Thedifference in length between wave-vectors k₄ and k₅ is due to thedifference in frequency of the underlying RF waves.

In short, the imaging receiver maps the 3D space of wave-vectors to a 2Dimage plane by projecting the former along the achromatic axis. Thisleads to chromatic aberration where some waves arriving from the samedirection are mapped to different points (e.g. wave-vectors k₄ and k₅ inFIG. 3C), and certain waves arriving from different directions map tothe same point (e.g. wave-vectors k₁, k₂, and k₃ in FIG. 3C).

The above statement can be understood with the help of FIG. 4, whichshows a portion of k-space. In this representation, every point is ak-vector (wave-vector) that corresponds to a plane wave arriving at thereceiver. The length of the k-vector (the distance of the point fromorigin located at the center of the semicircles in FIG. 4) isproportional to the frequency, and the angle of arrival of the wave isthe vector's direction. Given this one-to-one correspondence betweenwaves arriving at the receiver and the points in k-space, the latter ishelpful when describing the imaging receiver.

Accordingly, since the imaging receiver performs a projection along theachromatic axis, in k-space this projection takes a geometric meaning:points along each of the lines labeled as “Lines of constant k_(x)” inFIG. 4, are represented as a single point in the imaging receiver inthis example. FIG. 4 illustrates just five lines of constant k_(x) forsimplicity. The above perspective on the imaging receiver provides meansto generalizing the concept and enabling access to information that iscaptured by the distributed array. The imaging receiver may includestructure to implement one or more of the following features:

-   -   Sampling the incoming electromagnetic field at discrete points        using an array of antennas (120).    -   Upconversion of the received electromagnetic radiation to        optical domain at each of the sampled points. This is        accomplished with electro-optic modulators (130).    -   Conveying the upconverted signals, now in optical domain, using        optical fibers (140), one or more fibers per antenna, to a fiber        array.    -   Using fiber array that may be a scaled version of the antenna        array.    -   Free-space propagation (160) and optical processing of light        emanating from the output of the fiber array, which contains the        information on the received electromagnetic radiation.    -   Optical capture of the RF scene: The interference pattern within        composite beam 185, at every received RF frequency, may        correspond to the RF scene observed by the antenna array. The        optical capture of the RF scene may be processed to reconstruct        the RF scene.

As described herein, information about radio frequency (RF) emittersfrom received electromagnetic radiation may be extracted. The exemplaryimplementations may provide real-time, simultaneous determination ofcarrier frequency, amplitude and angle of arrival (AoA). In someembodiments, instantaneous bandwidth (IBW) may approach 100 GHz. Thiscapability may be achieved without sacrifice of signal-to-noise ratio(SNR), by virtue of an antenna array whose gain more than compensatesfor the added thermal noise that accompanies such wide IBW. The opticalapproach may enable the array's entire field of regard (i.e. its fullbeam steering range) to be continuously detected and processed in realtime.

Optical image formation and engineered spectral dispersion may be usedto acquire multiple k-space projections of the RF scene. Opticalupconversions of RF signals by high performance modulators enables theuse of simple, inexpensive optical components to perform correlationsamong the signals received by the array elements. For the IBW andresolution (in both frequency and AoA) provided with this approach, suchcorrelations would be intractable using a conventional approach based ondownconversion, channelization, A/D conversion and computationalcorrelation. For example, 8-bit digitization of 100 spectral channels,each 100-MHz wide and together spanning 10 GHz, for 1000 simultaneousspatial directions (array beams) requires 20 TB/s of data throughput,not to mention the computational burden of analyzing all that data inreal time, nor the sheer size and scale of 1000 parallel channelizedreceivers.

The optical approach may include the following: RF signals are receivedby antennas 120 that feed modulators 130, which upconvert the signalsonto optical carriers conveyed by fibers 140. The sidebands are launchedinto free space as a composite optical beam 160 through an output fiberbundle that replicates the arrangement of antennas 120 in the array, atreduced scale. In this way the optical output of the bundle comprises ascaled replica of the RF field incident on the antenna array aperture.In some embodiments, the output of the fiber bundle need not replicatethe arrangement of the antennas 120. Simple optical lenses and a camera(focal plane array of detectors 190) can then be used to capture theinterference pattern of the composite optical beam 160, from which anoptical image of the RF scene may be obtained (i.e. a map of the AoA andamplitude of any and all RF emitters sensed by the antenna array 120).The optical image of the RF scene may be obtained with straightforwardcomputational processing. To add frequency determination to this imagingcapability, the lengths of the output fibers are made unequal, so as tointroduce a controlled chromatic dispersion (e.g. linearly ramping thelength across the array, which is effectively an RF diffraction grating,or implementing lengths that have no correlation (e.g., may be randomlengths) across the array), spreading the frequency content of thesignals out in the image seen at the camera. Alternatively, or incombination with making the lengths of the optical fibers unequal, thespreading of the frequency content may be achieved by distributing theantennas in a non-coplanar configuration. This spreading of thefrequencies mixes the spatial and spectral information about a signal inthe image. The modulator outputs may be split into multiple fibers, andmultiple output fiber bundles may be used to form multiple images. Eachoutput fiber bundle may contain a different distribution of the fiberlengths, by which each corresponding image represents a differentprojection of the full spatial-spectral scene.

The most appropriate conceptual framework for understanding this processis k-space. Every RF signal incident on the array can be characterizedby a wavevector k, also called a k-vector. K-space is just a uniformequivalent of an abstract space comprised of up to 2 dimensions of AoA(azimuth and elevation) and 1 dimension of (temporal) frequency.Recalling that the magnitude of the wavevector is directly related tofrequency according to 2πf=ck, one can readily see that frequency andAoA represent a set of spherical coordinates spanning k-space. Thinkingin terms of wavevectors, rather than AoA and frequency, we are free toanalyze the scene using other coordinate systems, e.g. Cartesian:{k_(x), k_(y), k_(z)}. Each of the multiple images can be interpreted asa different projection of the full k-space. For example, when all fiberlengths are equal, this corresponds to a projection onto the aperture(x-y) plane, which is insensitive to k_(z), as shown in FIG. 4.Variation of the lengths provides different projections. As intomography in real (position) space, which builds 3D images of theinterior of structures by combining multiple projections, computationalreconstruction techniques can be used to build the full k-spacedistribution of RF emitters from the multiple projections. From thisk-space “scene,” the frequency and AoA of each individual emitter can beextracted.

Analysis and simulations show that with this approach, received signals'carrier frequency can be determined to ≈100 MHz or better, depending onthe variation of the lengths of the fibers and signal-to-noise ratio,and this can be accomplished simultaneously for multiple signals atwidely disparate frequencies, while simultaneously providing AoA aswell. The precision of the AoA determination depends on the ratio of thecarrier wavelength to the overall aperture size, as well as SNR: as anexample, in the low-noise limit, <1° accuracy can be obtained with a6-cm array aperture at 18 GHz.

Generalization of Imaging Receiver

The disclosed imaging receiver may be in accordance with one or more ofthe following features:

-   -   Allowing variation of the fiber length amongst the different        optical channels.    -   Allowing multiple optical fibers per antenna.    -   Allowing arbitrary geometry of the fiber array, not necessarily        linked to the geometry of the antenna array.    -   Allowing the geometry of the antenna array not to be flat (2D);    -   antennas in the array may be distributed in three dimensions,        for example following a contour of a curved surface.    -   Computational reconstruction of the RF scene that includes        extracting both the angle of arrival and frequency of the        incoming RF radiation.

The interference pattern produced by light emanating from the opticalfibers may no longer correspond directly to the RF scene. Instead, thefollowing general relation holds between the RF sources and the detectedoptical powers

P _(n) =a _(n) ·S  (1)

where a_(n) is a (abstract) vector corresponding to the n-th opticaldetector, S is a (abstract) vector corresponding to the distribution ofsources in the k-space, i.e. the RF scene, and P_(n) is the powerdetected by the n-th detector.

Expression (1) can be manipulated to obtain the following equivalentforms

$\begin{matrix}{{{P_{n} = {\sum\limits_{m}{a_{nm}S_{m}}}}{P =}}{AS}} & (2)\end{matrix}$

where the first of Eqs. (2) explicitly shows the summation of the dotproduct in Eq. (1) whereas the second of Eqs. (2) shows a compactnotation involving matrix multiplication of (sought) vector S by matrixA to obtain the measured vector P of detected optical intensities. InEq. (2), matrix A is determined by the details of the imaging receiverthat include the geometry of the antenna array, the geometry of thefiber array, and the lengths of the fibers, as well as any additionaloptical phases applied to the optical signals conveyed by the opticalchannels. Vector S describes the RF scene in k-space, i.e. thefrequencies (or frequency distributions), angles of arrival andintensities of the RF sources whose signals are received by the antennaarray. Vector P comprises the intensities measured by thephotodetectors. Hence, the reconstruction of the RF scene based ondetected (measured) optical intensities P may require the ‘inversion’ ofthe relation Eq. (2). Since matrix A may in general be rectangular (notsquare) and/or singular, such ‘inversion’ may not be well defined ingeneral. In this case, an approximate, and ‘most likely’ vector S issought that satisfies Eqs. (2) or Eq. (1). Note also that in Eq. (2),finding the left inverse of matrix A would be sufficient to reconstructthe scene.

There exist a variety of methods that can be used to find S thatsatisfies, or approximately satisfies, Eqs. (2) or Eq. (1) givenmeasured/detected P. For example, methods used in computed tomographymay be employed that include the algebraic reconstruction technique(ART) also known as Kaczmarz method, or its multiplicative version(MART), or their more sophisticated flavors known to those skilled inthe art. Such methods may maximize the entropy, or the relative entropy,or Kullback-Leibler divergence, of the reconstructed RF scene, or, inother words, may find the most likely distribution of RF sources(frequencies, intensities and angles of arrival of the received waves)that would result in the detected values of P. Also, ‘inverting’ arelation akin to that of Eq. (2) is encountered in compressive-sensingreconstruction. Therefore, methods used in that field may be applicablehere.

To facilitate and speed up the reconstruction of RF scenes, a look-uptable can be constructed by, for example, direct sensing of known sceneswhich can be augmented by computational processing using knowntomography techniques, as described above, on selected matrix entries asnecessary. The look-up table may receive inputs comprising one or morepixel coordinates corresponding to the location(s) of detected light bythe photodetector 190. Based on receiving these pixel coordinate inputs,the look-up table may output one or more k-space vectors, each k-spacevector identifying the frequency and AoA of a corresponding RF source ofthe RF scene. In some examples, the look-up table may also receiveinput(s) of the intensity of the detected light by the photodetectorcorresponding to each of the one or more pixel coordinates and outputk-space vector(s) based on such intensity input(s).

FIG. 6 shows an example of RF scene reconstruction using a linear arraywith randomized antenna position and a random distribution of fiberlengths. On the left is the original (input) distribution of four RFsources present in the scene as represented in k-space. On the right isthe reconstruction of the scene by inverting relation (2). Excellentreconstruction fidelity is accomplished in this case.

FIG. 7 shows the distribution of baselines used in the reconstruction ofFIG. 6. The baselines are provided by the fiber-length differences (Δt)and by the separations in the x-direction (Δx) of the antennas in thearray.

The above describes the general mode of operation of the cuing receiver.There may be other modes of operation that may relax the computationalburden of extracting the information about the RF scene. Below, examplesof some of such modes of operation are described in some detail.

Homothetic Arrays

FIG. 2D illustrates details of an embodiment where the detector 190 maycapture in real-time an image (still image and/or video image) of aselected frequency of the RF scene with non-selected frequencies beingeffectively filtered and treated as noise by the detector 190. In thisexample, one fiber per antenna may be used and the geometry of the fiberarray bundle at lenslet 150 (at the ends 141 of the optical fibers 140)may be a scaled version of the antenna array 120. For example, the ends141 of the optical fibers 140 may have the same relative physicalarrangement as the arrangement of the antenna array 110. For example, aprojection of the antenna array 110 onto a plane may have the samerelative arrangement as the arrangement of the ends 141 of opticalfibers 140 corresponding to the connection of such optical fibers 140 tothe associated antennas 120 of the array 110. The same relativearrangement may include the same relative spacing, same relative orderand/or same relative locations with respect to neighboring fiber ends141.

As shown in FIG. 2D, a phase offset 204 is applied to optical modulator130 by applying a constant (DC) bias voltage; to obtain optical phasedelay, voltage V=(/*V is applied, where V is the half-wave voltage ofthe electro-optic modulator. The phase offset 204 is variable and isbased on a selected frequency 202 input to the processor 200 and on the(optical) length of the optical fiber 140 a. The processor 200 outputsan appropriate phase offset 204 for each of the modulators 130 of theimaging receiver 100 to compensate for the phase delay the RF signalwould experience when traversing the distance L_(140a), which is equalto _(m)*L_(140a)/c, where m is the selected RF frequency 202, L_(140a)is the optical length of the fiber 140 a (time delay multiplied by thespeed of light) and c is the speed of light. Note that the appliedoptical phase offset to cancel the accrued RF phase delay need only beapplied modulo 2. Since the phase delay, _(m)*L_(140a)/c, of the RFsignal is an explicit function of the selected frequency 202, m, theapplied optical phase compensation provides phase cancellation only forthat selected RF frequency. Similarly, different optical lengthsL_(140a) require different optical phase compensations.

With these phase offsets applied to each of the modulators 130, despitethe different lengths of the optical fibers 140, the upconverted opticalsignals corresponding to the selected RF frequency remain in properphase relations at the outputs 141 of the optical fibers 140 for theoptical interference (e.g., constructive and destructive interference)in the composite beams 160 and 185 to reproduce the RF scene at thisselected RF frequency as an optical image on the detector 190 (as stilland/or video image). This way, the image projected onto and detected bythe detector 190 corresponds to the RF scene of the selected RFfrequency received by antenna array 110. However, optical signalscorresponding to RF frequencies outside this selected RF frequency willexit the optical fiber bundle without compensation for the phasedifferences caused by the different lengths of the optical fibers 140 inthe optical fiber bundle and thus will be distributed across thedetector 190 and appear as noise to the detector 190.

With the phase compensation as described with respect to FIG. 2D, the RFscene at the selected RF frequency is faithfully reconstructed in theoptical domain, i.e., the interference pattern generated by theoverlapping optical beams emanating from the fiber array corresponds tothe RF scene at the selected frequency, plus distributed background(fixed-pattern ‘noise’) due to sources operating at other frequencies.As such, little or no additional (computational) processing is needed todetermine the angle of arrival of waves at this frequency. Sourcesoperating at frequencies different than the selected one contribute tothe detected power, but their contribution is, in general, spread overmultiple detectors. As a result, the contribution of such sources to thesignal at any selected photodetector corresponding to a particular angleof arrival would be suppressed as compared to the frequency the receiveris ‘tuned to.’ Such contribution from out-of-band sources may be furthersuppressed by applying spectral filtering at the RF front end, i.e.before the up-conversion of the received RF signals to optical domain.Also or alternatively, optical filtering to suppress the contributionfrom out-of-band sources may be used.

In the exemplary implementation above, optical fibers with varyinglengths were utilized. However, other means for effecting phasevariation can be utilized. For example, true time delay lines—eitheradjustable or fixed—can be utilized to introduce length variation.Adjustable time delay provides the benefit of adjusting or fine tuningsystem operation on the fly.

The selected RF frequency 202 at which faithful optical reconstructiontakes place (detected as an image by detector 190) may be selected by auser based on certain RF frequencies of interest and/or automaticallychanged rapidly by applying suitable bias or phase offset to themodulators. Hence, the received frequency may be scanned to reconstructthe distribution of RF sources in the k-space, i.e. finding thefrequencies, intensities and angles of arrival of the receivedelectromagnetic waves.

Multiple Independent k-Space Projections

As indicated in FIG. 4, equal fiber lengths in combination withhomothetic arrays yield a particularly simple projection of the k-spacein the optical reconstruction. On the other hand, purely randomselection of fiber lengths yields projections of the type indicated inFIG. 5. By choosing the fiber lengths to vary linearly with the positionof the antenna in the array, and homothetic arrays configuration, theprojection of the k-space that deviates from that of FIG. 4, but onethat is less complex than that of FIG. 5 may be obtained. Such acuing-receiver configuration is shown in FIG. 8. One can think of suchconfiguration as receiving all incoming RF radiation on one side of theachromatic axis.

As an example, in FIG. 8, the optical-fiber length corresponding to theantenna element at the top of the array is shorter than the opticalfiber-fiber length corresponding to the element at the bottom. (It isnoted that the fiber-length differences in FIG. 8 are shown forillustration purposes only, and may be considerably different in anactual implementation of the system.) As a result, an RF wave incomingalong the line labeled in FIG. 8 as “Achromatic axis” would produce anoptical wave-front parallel to the optical axis of the imaging lens, hadit not been outside the field of view. On the other hand, the wavelabeled as “incoming RF” would produce a spot off axis as shown in thefigure.

The manifestation of such receiver configuration in k-space is shown inFIG. 9. Compared to the configuration of equal-length fibers of FIG. 4,the projection lines are tilted in the k-space. As a result, mixing ofthe angle of arrival and frequencies occurs in the light distributiondetected by the photodetector array. It is also possible to configurethe array in such a way that the RF imaging axis (achromatic axis) fallsoutside the field of view of the antenna elements as shown in FIG. 8.Note that the field of view is determined by the acceptance angle of theindividual elements of the antenna array.

Combining two receivers with different RF imaging axes, as in FIG. 10,yields two images of the same RF scene with differentfrequency-dependent shift in the optical reconstruction: Note that forthe same two RF sources operating at frequencies Ω₁ and Ω₂, the image ofsource 1 is shifted down with respect to source 2 in imager with RF axisA, whereas it is shifted up in the imager with RF axis B.

In an abstract sense, the use of two arrays with different RF imagingaxes can be visualized with the help of FIG. 11A. The 3D space ofpropagation vectors k is projected onto two dimensions along axes A andB corresponding to the two arrays. Accordingly, two 2D images are formedin the optical domain with the 3D k-vector corresponding to an incomingRF wave represented as a 2D vector in each of the arrays. Having the two2D projections, the original 3D k-vector can be reconstructedcomputationally. This way, full information of the incoming wave, i.e.the AoA and the frequency, can be recovered from the two 2D images.

The reconstruction of the 3D k-vector from two 2D projections can becompared to 3D real-space stereoscopic imaging, FIG. 11B. In that case,the image projected on the retina of each eye is two-dimensional, yet a3D representation of the scene is reconstructed ‘computationally’ in thebrain from two such images obtained by two projections along two opticalaxes of the left and right eyes. Similar computational reconstruction ofthe 3D k-vector space is performed in exemplary implementations of ourinvention.

FIG. 13 is another illustration of the two projections of k-space. Twosets of projection lines are present, each set corresponding to one ofthe achromatic axes, see FIG. 12.

Although the 3D k-space reconstruction of the exemplary implementationsare conceptually similar to the stereoscopic vision described above,there may be differences between these two cases. Whereas stereoscopicvision applies to imaging objects in real space, our system may apply tok-space—the space of k-vectors corresponding to plane waves. As aresult, for the stereoscopic vision to be effective, the two parts ofthe imaging system must be offset spatially, as in the familiarLeft-eye/Right-eye configuration of FIG. 11B; this is how the imagingaxes are made non-parallel, and each eye presents a different view ofthe same subject. In contrast, since the imaging receiver performsprojection in k-space, the two antenna arrays of the imaging receiver inFIG. 10 can be co-located as long as they present different imaging axesby, for example, properly choosing the optical fiber lengths.

The ability to co-locate the two arrays can be taken advantage byinterleaving the antenna placement as in FIG. 12. This configuration canbe thought of as consisting of a single antenna array with fiberscollected in two separate bundles to form two optical images; each ofthe fiber bundles carries RF signals from antenna elements scatteredthroughout the array. The fiber lengths for each of the bundles arechosen so as to yield RF axes A and B, FIG. 12, similar to the RF axesof the two spatially-separated arrays of FIG. 10.

The idea of co-locating the two arrays can be implemented as shown inFIG. 14 where a single antenna array is present. The modulated opticaloutput of each antenna element is split into two, and the resulting twosets of fibers are collected into two fiber bundles to reconstruct twooptical images. The lengths of the fibers in each of the bundles arechosen so as to produce different RF optical axes, labeled as RF axis Aand RF axis B in FIG. 14. As a result of having originated from twodifferent RF imaging axes, the two optical images correspond to twodifferent projections of the 3D k-space, as explained in FIG. 11A, andtherefore provide means to reconstructing the AoA and frequency ofreceived RF waves.

For imaging receivers configured in such a way that the RF imaging axesfall outside the field of view of individual antennas, the system can befurther simplified by combining optical reconstruction. Since thek-vector of the received incoming RF wave always falls to one side ofthe RF imaging axis, the resulting optical image will fall to one sideof the optical axis. As a result, the two optical images form on theopposite sides of the optical axis. This allows combining the twooptical systems into one where half of the image corresponds to theprojection of the k-space along RF axis A, and the other halfcorresponds to the projection of the k-space along RF axis B.

The disclosed exemplary implementations may resolve the ambiguity in theangle of arrival (AoA) of electromagnetic radiation at the position of adistributed aperture. In addition, it provides information about thefrequency of received radiation. The exemplary implementations may do sowithin the framework of imaging receiver concept wherein the incoming RFis up-converted to optical domain in the front end, i.e. at theindividual antenna elements that constitute the receiving array, andconveyed with optical fibers to central location for processing.

The exemplary implementations allow the use of relatively slowphoto-detector array for detector 190, one that need not respond at theRF frequencies received, to extract information about the RF sourcelocation (AoA) and the transmitted frequency. Although the disclosedexemplary implementations will also operate with the use of a relativelyfast photo-detector array for detector 190, it is not necessary and mayconstitute a wasted extra expense. As described herein, each of theplural fiber optic bundles may have their optical outputs 141 imaged bythe same detector 190 simultaneously or may each have their opticaloutputs 141 imaged by a different detector 190. In addition, the pluraloptical bundles may have their optical 141 outputs imaged separately andsequentially (e.g., rapidly switch the optical outputs 141 of eachoptical bundle on and off to detect the optical outputs at differenttimes by detector 190). This latter implementation may be helpful whenattempting to resolve ambiguities in analysis of certain opticalpatterns detected by detector 190 of the combined optical outputs 141 ofplural fiber optic bundles onto detector 190.

To the best of our knowledge, prior to this invention, there was no wayto resolve the frequency/AoA ambiguity within the imaging-receiverframework, absent post-detection (using fast photo-detector(s))electronic processing to determine the incoming frequency.

The exemplary implementations may unambiguously pin-point the locationand frequency of an RF source with the imaging receiver.

The implementation of the general imaging receiver may require intensivecomputation to achieve faithful reconstruction of the RF scene. On theother hand, the use of ‘stereoscopic’ reconstruction with multipleprojections of the k-space may in some circumstances lead to ambiguousreconstruction. For example, if multiple RF sources are transmittingsimultaneously in the scene, there remains the possibility of assigningincorrect AoA and frequency in some circumstances. Such possibility canbe related to the stereoscopic vision, compare FIG. 11B, which in mostcases is sufficient to faithfully reconstruct a 3D scene, but allowsoptical illusions in some circumstances, with false impression of objectplacement and/or orientation in the scene.

This disadvantage can be overcome by increasing the number of arrayssimultaneously trained on the scene (e.g., three or four or morearrays), with each array presenting a different RF imaging axis. Eachadditional array introduces additional constraints on the coincidentalplacement of RF sources and their frequencies that could lead toambiguity. Therefore, each additional array reduces the likelihood ofsuch a coincidence happening. Such arrangement can be compared totomography where a series of projections at various angles, acomputer-tomographic (CT) scan, allows the 3D reconstruction in realspace. Since our invention relates to k-space, such reconstruction canbe referred to as k-space tomography in our case. The reduced ambiguityis at the cost of increased computational complexity to reconstruct theRF scene.

FIG. 16 is a flow chart of a method performed by an imaging receiverconfigured in accordance with the disclosed exemplary implementationsand FIGS. 1, 2A-C. In S1600, sampling of the RF signal field received atdistributed antenna arrays is performed. In S1610, the sampled RFsignals are modulated onto optical beams, and in S1620 the modulatedsignals are conveyed by, for example, optical fibers having varyinglengths in accordance with S1630 so as to generate interference patternsamongst the modulated optical beams in S1640. The optical beaminterference is recorded by photodetectors in S1650 and computationalreconstruction of the RF signals in k-space is performed in S1660 usingknown techniques.

One way of providing the different path lengths, per S1630 in FIG. 16,is by using optical fibers having varying lengths carrying the modulatedoptical beams to the photodetectors for each optical beam. In oneexemplary implementation, the length of the fibers varies linearly inaccordance with its position at the antenna/modulator array. Analternative methodology would be to use different configurations for thefiber array as compared to the antenna array. Another alternative wouldbe to use arbitrary, e.g. random, fiber lengths as illustrated in FIG.5. The range of fiber lengths may affect the spectral resolution of theobtained reconstruction of the RF scene. Thus, the spectral resolutionmay be determined by the largest difference in fiber length inaccordance with well-known scientific principles. For example, if thelargest fiber length difference leads to the relative delay betweenrespective optical signals of 1 ns, then the spectral resolution, i.e.the ability of the system to distinctly resolve RF sources emitting atadjacent frequencies, may be about 2*(1 ns)⁻¹=2 GHz. The practical pathlength variations implemented in optical fiber may range between 0.5 mmand hundreds of meters.

K-Space Projections in RF Domain

In alternative embodiments, conversion of the RF (radio frequency)radiation detected by the antenna array 110 to the optical domain may beavoided, with the detector 190 of FIG. 1 replaced with a plurality of RFdetectors (or electrical power detectors). In the k-space receiverdescribed above, the interference module (the interference module is thestructure of FIG. 1A between the antenna array 110 and photodetectorarray 190) is implemented with an optical channel where the RF signalsdetected by antennas 120 are converted to light, and subsequent timedelays and cross-coupling (mixing, interference) of the received signalsis performed in optical domain. In the below described alternativeembodiments, the interference module is implemented in the RF domain.Although these alternative embodiments implement the interference modulein the RF domain, other frequency domains may also be used to implementthe interference module, such as in the acoustic domain, and the belowdescription should be recognized to equally apply to non RF domainimplementations.

The frequency of the RF radiation (detected by the antennas 120 andtransmitted as an electrical RF signal) may be any radio wave frequency,including any radio frequencies from high frequency millimeterwavelength RF (30 to 300 Ghz) to low frequency (LF) (30 kHz to 300 kHz)and to very low frequency (VLF) RF (3 kHz to 30 Khz), and anything inbetween. Transmission loss when transmitting the RF signals from theantennas 120 may be acceptable, although lower transmission loss may beobtained as the frequency of the RF signal is made lower. For example,for RF signals frequencies below 50 GHz, transmission loss in a coaxcable may be acceptable (1.44 dB/ft at 50 GHz) to implement varieddelays of the transmitted RF signals prior to coupling the same in an RFcoupler (as described below).

FIG. 17A illustrates an exemplary configuration where RF radiationdetected by antennas 120 of the antenna array 110 are transmitted alongRF waveguides 140 a to RF coupler 300. After interference of the RFsignals via the RF coupler 300, resultant signals are output from the RFcoupler 300 and conveyed by RF waveguides 140 b to a plurality of RFdetectors 190 a. Each RF detector 190 a detects the corresponding RFsignal received via one of the waveguides 140 b and outputs anelectrical analog envelope signal corresponding to the power of thereceived RF signal. The plurality of analog envelope signals areprovided by wiring 190 c to corresponding analog to digital converters190 b. Analog to digital converters 190 b convert each of the receivedanalog envelope signals to a corresponding digital value that aresubsequently transmitted to processor 200. An analog to digitalconverter 190 b may be provided for each analog envelope signal outputby the RF detectors 190 a, or an analog to digital converter 190 b maybe shared by several of the RF detectors 190 a by providing pluralanalog envelope signals to a multiplexer (not shown) which is thencontrolled to select and sequentially transmit each of the input analogenvelope signals to the shared analog to digital converter.

Processor 200 may perform the same processing as described herein, suchas determining the k-space information of one or more RF sources in theRF scene (i.e., the angle of arrival, which may be expressed as, e.g.,azimuth and elevation, and frequency of one or more RF sources in the RFscene). K-space information of the RF sources/RF scene may be processedand provided in real time by the antenna array, the interference module(including waveguides 140 a and RF coupler 300 in this example), RFdetectors 190 a, analog to digital converter 190 b and the processor200. Depending on the RF waveguides used, the frequency of operation ofthis embodiment may be limited compared to the optics-based approach dueto propagation losses in the RF waveguides (which increase as thefrequency is increased). However, bypassing optics reduces thecomplexity of the system, and therefore its cost, while its simplicitymay help improve reliability.

In some examples, the RF signals detected by antennas 120 may bedownconverted to a lower frequency and this lower frequency RF signalmay be transmitted and processed by RF coupler 300. The RF signaldetected by antennas 120 may be downconverted by mixing the detected RFsignal with a sinusoidal signal provided by a local oscillator andapplying a low pass filter or a band pass filter to the resultant signalto allow transmission of the lower frequency sideband. In thisalternative implementation, downconversion may be performed by mixers,each interposed between the electrical RF signal output by acorresponding antenna and waveguides 140 a. Such mixers may beimplemented in a similar manner to that shown in FIG. 1A with respect touse of the electro-optic modulators 130 of FIG. 1A, but the mixersmodulate the received RF signal output by the corresponding antenna 120to a lower frequency electrical signal with a sinusoidal electricalsignal (replacing light received via laser 125 and splitter 127 of FIG.1A). A low pass or band pass filter may be interposed between mixers andwaveguides 140 a to transmit the lower frequency sideband and filter(block) a resultant higher frequency sideband.

In other examples, the RF signals detected by antennas 120 may beupconverted to a higher frequency, and this higher-frequency RF signalmay be transmitted and processed by RF coupler 300. The RF signaldetected by antennas 120 may be upconverted by mixing the detected RFsignal with a sinusoidal signal provided by a local oscillator andapplying a high-pass filter or a band pass filter to the resultantsignal to allow transmission of the higher frequency sideband. In thisalternative implementation, upconversion may be performed by mixers asdescribed above for downconversion.

RF waveguides 140 a in these embodiments replace the optical fibers(e.g., optical fibers 140) that transmit and emit light to form combinedbeam 185 (e.g., in free space) as described in the embodiments above.The lengths and spatial positioning of the RF waveguides 140 a (e.g.,with respect to the antennas 120 of the antenna array 110) maycorrespond to the lengths and spatial positioning of these opticalfibers in any of the embodiments described above. Although FIG. 17Aimplies that the lengths of the RF waveguides 140 a are the same, itwill be appreciated that the lengths of the RF waveguides 140 a may havevaried lengths, such as described herein with respect to optical fibers.For example, the lengths of the RF waveguides may be a function of theposition of the antenna 120 whose signal they transmit, such that thelengths of the RF waveguides 140 a vary linearly with the position ofthe antenna in the array, such as described herein with respect to FIGS.8-15. The lengths of the RF waveguides 140 a may be uncorrelated, andmay have a random distribution and/or a variety of lengths. Further, thespatial positions of the RF waveguides (at their output to the RFcoupler 300) may not have the same relative positions of (or otherwisecorrelate to) the positions of the antennas 120 of the antenna array110. For example, the lengths and spatial positions of the RF waveguides140 a may correspond to the lengths and spatial positioning describedherein with respect to FIGS. 5-7. Alternatively, the lengths of the RFwaveguides 140 a may be the same and have a relative spatial positioning(at their output to the RF coupler 300) that is relatively the same asand/or aligns with the spatial positions of the antennas 120 (such asdescribed with respect to FIG. 4).

Each of the optical domain embodiments (where the RF signal of anantenna is converted to a corresponding optical signal) disclosed hereinmay be implemented in the RF domain (without converting the RF signal toa corresponding optical signal). The details set forth above withrespect to these optical domain embodiments that are applicable to theRF domain alternative implementation (e.g., waveguide lengths, waveguidespatial arrangement, signal interference and data processing) may be thesame for the RF domain implementation and may not be fully repeatedhere.

FIG. 17C illustrates an example where the lengths of the RF waveguides140 a are varied and have a spatial positioning at their output to theRF coupler 300 that is not in the same arrangement as the spatialpositioning of the corresponding antennas 120 of the antenna array 110to which the RF waveguides 140 a are connected. Each of the RFwaveguides 140 a may be embodied as flexible wiring (for example,coaxial cables or twisted pairs of wiring) carrying an RF signalprovided by the antenna 120 to which the RF waveguide 140 a isconnected. However, other types of RF waveguides, such as thosedisclosed herein, may also be used. Each of the RF signals provided byantennas 120 of the antenna array 110 may be amplified with acorresponding amplifier (not shown) that may be inserted between theantenna 120 and the RF coupler 300 (such as at the output of the antenna120).

To allow interference of the RF signals from the antenna array 110,shielding of each of the RF waveguides 140 a may be removed at the RFcoupler 300. At the RF coupler 300, the electromagnetic fieldcorresponding to the RF signal received from an antenna 120 and carriedby the corresponding transmission line overlaps with the electromagneticfields corresponding to the RF signals carried by other, neighboringtransmission lines that similarly are carrying RF signals from differentantennas 120 of the antenna array 110. Such field overlap may yield across-talk, or coupling, among the different transmission lines suchthat each of the outputs of the RF coupler 300 carries signals frommultiple inputs to the RF coupler. Exemplary RF couplers 300 a and 300 billustrated in FIGS. 18A and 18B provide two such examples of suchstructure. FIG. 18B is similar to FIG. 18A but includes additionalsignal wires inserted between those connected to and carrying RF signalsfrom a corresponding one of the antennas 120, allowing such additionalsignal wires to receive RF radiation from the input RF signals, andoutput an electrical signal to RF detectors 190 a. FIG. 18C can beconsidered an extreme case of FIG. 18A or 18B, where the signalconductors of the transmission lines are placed so close to one anotheras to make a physical and electrical connection, thereby forming asingle electrode in the coupling region.

In some examples, shielding of the RF transmission lines of the RFwaveguides 140 a and/or 140 b may not be necessary, so that interferencemay occur (either to a strong or weak degree) between the RFtransmission lines as the RF signals are transmitted from the antennaarray 110 to the RF coupler 300 and/or from the RF coupler 300 to the RFdetector 190 a. In these examples, the RF coupler 300 may “replace” oneor both of waveguides 140 a and 140 b, although RF coupling at certainlocations along the transmission of the RF signals may be weak (wherethe function of the structure may be more oriented to transmissionrather than RF coupling).

Rather than providing a continuous transmission line between the antennaarray 110 and the RF detector 190 a through RF coupler 300, transmissionlines of the waveguides 140 a from the antenna array 110 may terminateat their input to the RF coupler 300 and resume at the output of the RFcoupler 300 as part of waveguides 140 b. For example, the RF signals maybe allowed to radiate into free space or other medium to interfere withone another, and resultant electromagnetic signals are each received andconverted into an RF signal by wiring positioned to receive the radiatedelectromagnetic signals (e.g., acting as antennas at a downstreamlocation from the free space or other medium). Further discussion andexemplary details of the RF coupler 300 are set forth below.

Referring back to FIG. 17B, after the RF signals interfere with oneanother, the resultant RF interference pattern is detected by RFdetectors 190 a and converted to a digital form by analog to digitalconverters 190 b and sent to processor 200.

The interference pattern produced by the RF coupler 300 may no longercorrespond directly to the RF scene. Instead, the general relation ofEq. (1) holds between the RF sources and the detected RF signals by RFdetector 190 a, repeated below:

P _(n) =a _(n) ·S  (1)

where a_(n) is a (abstract) vector corresponding to the n-th RFdetector, S is a (abstract) vector corresponding to the distribution ofsources in the k-space, i.e. the RF scene, and P_(n) is the powerdetected by the n-th RF detector.

As noted, expression (1) can be manipulated to obtain the equivalentforms of Eqs. (2), repeated below:

$\begin{matrix}{{{P_{n} = {\sum\limits_{m}{a_{nm}S_{m}}}}{P =}}{AS}} & (2)\end{matrix}$

where the first of Eqs. (2) explicitly shows the summation of the dotproduct in Eq. (1) whereas the second of Eqs. (2) shows a compactnotation involving matrix multiplication of (sought) vector S by matrixA to obtain the measured vector P of detected RF intensities. In Eq.(2), matrix A is determined by the details of the system including thegeometry of the antenna array, the geometry of the RF waveguides 140 a,140 b array, RF coupler 300, and the lengths of the waveguides 140 a, aswell as any additional RF phases applied to the RF signals conveyed bythe RF channels. Vector S describes the RF scene in k-space, i.e. thefrequencies (or frequency distributions), angles of arrival andintensities of the RF sources whose signals are received by the antennaarray. Vector P comprises the intensities measured by the RF detectors190 a. Hence, the reconstruction of the RF scene based on detected(measured) RF intensities P may require the ‘inversion’ of the relationEq. (2). Since matrix A may in general be rectangular (not square)and/or singular, such ‘inversion’ may not be well defined in general. Inthis case, an approximate, and ‘most likely’ vector S is sought thatsatisfies Eqs. (2) or Eq. (1). Note also that in Eq. (2), finding theleft inverse of matrix A would be sufficient to reconstruct the scene.

FIGS. 19A-19E illustrate details of exemplary RF couplers 300. It shouldbe emphasized, that reference to RF coupler “300” may be a genericreference which may apply to any and all of the exemplary RF couplersdescribed herein (e.g., 300 a, 300 b, 300 c, 300 d, 300 e, 300 f andtheir alternatives). In FIG. 19A, an RF coupler 300 c may be implementedas a microstrip transmission line (or, simply, a microstrip), comprisingground plane 310, signal electrode 312 and dielectric 314 interposedbetween the ground plane 310 and the signal electrode 312. FIG. 19A (a)shows a single microstrip, which may comprise an input and/or an outputto the RF coupler 300 c and may be connected to a coaxial cable or othershielded RF waveguide at the input and/or output of the RF coupler 300c. The ground plane 310 may be a sheet (e.g., film) of a conductivematerial and the signal electrode 312 may be conductive wiring (e.g.,strip). It should be emphasized that the phrase “ground plane”references a relatively large conducting surface serving to confine theelectromagnetic field of the RF signals carried by the transmissionlines. While a ground plane may have a planar geometry, other shapes mayalso be used for a ground plane. It also should be recognized that theground plane may or may not be connected to a reference potential ofground. When waveguides 140 a and 140 b are implemented as coaxial cable(comprising an inner conductor surrounded by an insulating layer whichare both enclosed by a metallic shield), end(s) of the signal electrode312 may have a direct electrical connection to the inner conductor(s) ofthe coaxial cable(s), while the ground plane 310 and outer metallicshield of the coaxial cables may be connected to a constant referencepotential, such as to ground.

As shown in FIGS. 19A, (b) and (c) illustrate plural microstripscomprising signal electrodes 312 formed on the same dielectric 314 andon the same ground plane 310. Although only two microstrips areillustrated in FIGS. 19A (b) and (c), each of plural microstrips areconnected to a corresponding one of the waveguides 140 a and acorresponding one of the waveguides 140 b, e.g., as shown in anddescribed with respect to FIGS. 18A and 18B. FIG. 19A (b) illustratesthe spacing of the plural signal electrodes 312 relatively small, ascompared to that of FIG. 19A (c), allowing relatively stronger couplingof the RF signals transmitted along the neighboring transmission lines.For example, the distance between signal electrodes smaller than tentimes the thickness of the dielectric 314 may provide adequate couplingbetween the waveguides. More specifically, using 100-μm thickliquid-crystal polymer dielectric having the relative dielectricconstant of about 3, and signal electrodes 250-μm wide, at the frequencyaround 100 GHz, the separation between signal electrodes of less than 1mm may provide sufficiently strong coupling between the waveguides.Furthermore, to increase coupling, the separation between signalelectrodes 312 may be reduced to zero, as in the example of FIG. 18C, soas to provide electrical connection between the signal electrodes. Itshould be appreciated that FIGS. 19A (a), (b) and (c) may representdifferent portions of the RF coupler 300 (such as different portions ofRF coupler 300 a or 300 b illustrated in FIGS. 18A and 18B). Inaddition, the structures of FIG. 19A may also be used as the waveguides140 a and/or 140 b themselves. In some designs, it may be desired tolimit RF coupling to a certain portion of the system transmitting the RFsignals, and have only limited or insignificant RF coupling at otherlocations. By increasing the spacing between neighboring signalelectrodes 312 (as exemplified by FIG. 19A (c)), RF coupling may bedecreased between neighboring microstrip transmission lines.

Although only two transmission lines with their respective signalelectrodes 312 are illustrated in FIG. 19A (b) and (c), all of thetransmission lines of the RF coupler 300 may be formed on the samedielectric 314 and ground plane 310 as shown. Alternatively, themicrostrip transmission lines with signal electrodes 312 of the RFcoupler may be formed on multiple ground plane/dielectric stacks(310/314) in various arrangements. For example, the multiple groundplane/dielectric stacks (310/314) may be arranged to have the signalelectrodes 312 face each other (such as a stack of ground plane 310 a,dielectric 314 a, signal electrodes 312 a, signal electrodes 312 b,dielectric 314 b and ground plane 310 b in that order with a gap ordielectric interposed between signal electrodes 312 a and 312 b). FIG.19B illustrates one such example with two sets of microstrips 300 cfacing each other with a gap between the sets of microstrips 300 c. Thestructure of FIG. 19B can be considered as a particular implementationof a stripline, where one or more signal electrodes 312 are sandwichedbetween ground planes 310 (which may form a single electrical node).FIGS. 19C (a), (b) and (c) illustrate several examples of the RF coupler300 d formed with a stripline configuration, with signal electrodes 312of the transmission lines extending through a gap between two adjacentground planes 310. The ground planes 310 sandwich dielectric 314 whichsurrounds the signal electrodes 312. The ground planes may beelectrically connected and/or electrically and physically connected as asingle integral conductive structure by conductive sidewalls (not shown)at the edges of the ground planes 310 to form a hollow tube (aconductive cuboid, or if the ground planes are formed to have a shapeother than a geometrically planar shape, a hollow conductive cylinder orwith an elliptical cross section, etc.). FIG. 19C (a) illustrates asingle transmission line with signal electrode 312, while FIG. 19C (b)illustrates plural transmission lines with corresponding signalelectrodes 312 having a relatively close spacing as compared to therelatively wide spacing of FIG. 19C (c) to respectively increase anddecrease coupling of the RF signals carried by the transmission lines.Again, it should be appreciated that the illustration of only twostriplines with respective two signal electrodes 312 in FIGS. 19C (b)and (c) is for ease of illustration and explanation, and that more thantwo of the RF signals provided by antennas 120 of the antenna array 110may be connected to a corresponding transmission line within the samestripline structure (e.g., all the RF signals provided by the antennas120 via waveguides 140 a may be connected to transmission lines withsignal electrodes 312 that are sandwiched between two adjacent groundplanes 310 and/or transmitted through a hollow conductive tube, such as310′).

As noted, in some examples, the stripline configuration may comprise oneor more transmission lines 312 extending through a conductive tubeserving as the ground plane (which may be formed as a hollow cylinder,or hollow cuboid, or have some other shape). FIG. 19D illustrates onesuch example of an RF coupler 300 e comprising signal electrodes 312′extending through hollow conductive cylinder 310′ (which may beconnected to a reference potential, such as ground). The hollowconductive cylinder 310′ may be filled with a dielectric (not shown),which may be a solid insulator, liquid or gas (e.g., air). In thisexample, waveguides 140 a are implemented as coaxial cable. Innerconductors of each of the coaxial cable waveguides 140 a transition to acorresponding signal electrodes 312′ of the RF coupler 300 e (e.g., theinner conductors of the coaxial cables waveguides 140 a are eachelectrically connected corresponding signal electrodes 312′ which maytake the form of continuing to extend into the hollow conductivecylinder 310′ as the corresponding signal electrode 312′ without theexternal conductive shielding of the coaxial cable waveguide 140 a).Without individual shielding (as provided by the coaxial cableswaveguides 140 a) the electromagnetic field corresponding to the RFsignals transmitted along the signal electrodes 312′ within conductivecylinder 310′ may extend to overlap adjacent signal electrodes, andhence be coupled among the signal electrodes 312′ allowing the RFsignals to interfere with each other within the RF coupler 300 e.

At the output of the RF coupler 300 e, the RF signals, or electricalsignals (analog or digital) representing the power of the correspondingtransmitted RF signals, are transmitted by waveguides 140 b formed as aribbon cable (having a plurality of conductors, each electricallyconnected to a corresponding one of the signal electrodes 312′). Inalternative embodiments, the RF detector may be formed at the output ofthe RF coupler 300 e and the ribbon cable may transmit on each of itsconductors an analog signal corresponding to the power of a RF signalcarried by a corresponding one of the signal electrodes 312′ of the RFcoupler 300 e (where the analog signals are later converted to digitalform by analog to digital converters 190 b to which the ribbon cable 140b is connected. Alternatively, both the RF detector 190 a and the analogto digital converter 190 b may be formed at the output of the RF coupler300 e and the ribbon cable may transmit digital signals (in parallel orserial format, e.g.), each digital signal representing the detectedpower of an RF signal carried along a corresponding one of the signalelectrodes 312′ of the RF coupler 300 e.

In a modification of the embodiment of FIG. 19D, hollow conductivecylinder 310′ (and/or the conductive disk shaped caps enclosing ends ofthe body of the hollow conductive cylinder 310′) may be eliminated,resulting in an RF coupler 300 comprising the plurality of signalelectrodes 312′ extending through free space, such as air, or a soliddielectric.

FIG. 19E illustrates another example of an RF coupler. RF coupler 300 fmay be implemented as described and discussed above with respect to FIG.19D, but instead of the use of signal electrodes 312′ extending throughthe length of the a conductive tube 310′ of the RF coupler 300 e, thetransmission lines terminate within the conductive tube 310′ at theinput end of the RF coupler 300 f (left side of FIG. 19E) and resume atthe exit end of the RF coupler 300 f (right side of FIG. 19E). Thesignal electrodes 312′ may extend into the space of the hollowconductive tube 310′ a certain length, each protrusion of the signalelectrodes 312′ into the hollow conductive tube 310′ acting as amonopole antenna to radiate the corresponding RF signal (at the inputend of the RF coupler 300 f) and to receive a radiated RF signal (at theoutput end of the RF coupler 300 f). Although FIG. 19E only illustratesthe terminated signal electrodes 312′ at the output end of the RFcoupler 300 f, the same structure may be used at the input end of RFcoupler 300 f It will be appreciated that the number of transmissionlines at the input end may be less or more than the number oftransmission lines at the output end of the RF coupler 300 f, and/or thespatial arrangement (e.g., physical layout) of the terminatedtransmission lines 312′ may differ from each other at the input end andoutput ends of the RF coupler 300 f.

FIG. 19F illustrates exemplary details of an RF waveguide at the RFcoupler 300. The structure shown in FIG. 19F may be implemented withrespect to an input to the RF coupler (and thus represent RF waveguide140 a) and also may be implemented as part of an output from the RFcoupler (and thus represent RF waveguide 140 b). In this example, the RFwaveguide 140 a/140 b is implemented as a coaxial cable, comprisingconcentrically arranged protective outer plastic sheath 140-2surrounding a conductive electromagnetic shield 140-4 surrounding aninner dielectric 140-6 surrounding a signal electrode formed as an innerconductor 140-8. The inner conductor 140-8 may be solid, while theprotective outer plastic sheath 140-2, the conductive electromagneticshield 140-4 and the inner dielectric 140-6 may have tube shapes.

The end (either input end or exit end) of the RF coupler 300 is shown bydashed lines 310′ which may correspond to one of the conductive diskshaped caps enclosing ends of the body of the hollow conductive cylinder310′ (either at the input side or exit side of the RF coupler 300, suchas RF coupler 300 e or 300 f of FIG. 19D or 19E). The protective outersheath 140-2 and conductive electromagnetic shield 140-4 of the RFwaveguide 140 a/140 b terminate at the hollow conductive cylinder 310′of the RF coupler 300. A portion of the protective outer sheath isrepresented by dashed lines in FIG. 19F to help illustrate the structureof the coaxial cable implementation of the RF waveguide. Alternatively,the conductive electromagnetic shield 140-4 may extend partly or fullythrough hole 310′h in the hollow conductive cylinder 310′ and terminateat the hollow conductive cylinder 310′.

As shown in FIG. 19F, the inner conductor 140-8 extends into (and ispart of) the RF coupler 300, extending through hole 310′h in the hollowconductive cylinder 310′. In this example, the inner conductor 140-8acts as a signal electrode of an RF transmission line. When the coaxialcable is used as an RF waveguide 140 a, it transmits an RF electricalsignal from a corresponding antenna 120 to the RF coupler 300, and whenthe coaxial cable is used as an RF waveguide 140 b, it transmits an RFsignal resulting from interference of the RF signals provided by two ormore antennas 120. When implementing the RF coupler 300 e of FIG. 19D,the inner conductor 140-8 may extend fully through the hollow conductivecylinder 310′ (dashed lines extending from inner conductor 140-8representing this option). When implementing the RF coupler 300 f ofFIG. 19E, the inner conductor 140-8 may project from the inner wall ofhollow conductive cylinder 310′ and terminate at a distance chosen toallow radiation of the RF signal (e.g., about one quarter the wavelengthof the detected RF signal, which may be the same distance of a monopoleor a dipole forming one of antennas 120). Inner dielectric 140-6 mayextend through the hole 310′h to maintain separation between the innerconductor 140-8 and hollow conductive cylinder 310′. Outer conductiveelectromagnetic shield 140-4 may physically and electrically connect tothe hollow conductive cylinder.

FIG. 20 illustrates an example of an RF detector 190 a used to detectthe power of an RF signal received from a corresponding transmissionline of the RF coupler 300 (such as any of the RF transmission lines andRF couplers described herein). The RF detector 190 a is connected at itsinput to a corresponding transmission line at the output of the RFcoupler 300, with the corresponding signal electrode 312 having anelectrical connection to the anode of a diode D. The cathode of thediode is connected to the output of the RF detector 190 a, with acapacitor C and resistor R connected in parallel between the output andground. In operation, the diode acts as a half-wave rectifier andtransmits the positive voltage portion of the RF signal (a highfrequency AC signal (e.g., sinusoidal signal)) received from the RFcoupler 300 while blocking transmission of the negative potentialportion of the RF signal. The capacitor C smooths the voltage waveformoutput from the diode D by storing charge while resistor R allows acontinued gradual discharge by the capacitor C, thereby providing anoutput from the RF detector 190 b corresponding to the power of the RFsignal recently received. Because charge stored in the capacitor Creceived from the diode D dissipate to ground through resister R overtime, the output by the RF detector 190 a changes with time as the powerof the received RF signal changes. It will be apparent that otherrectifier circuits may be implemented than the single diode D as shownin FIG. 20, such as a full wave rectifier circuit.

FIG. 21 illustrates an exemplary method that may be implemented by theabove described RF domain k-space detectors. In general, betweensampling the incoming electromagnetic radiation by the antennas 120 ofthe antenna array 110 and the array of RF detectors 190 b, aninterference module is provided that has an array of inputs and array ofoutputs, and affords the following: (1) each output of the RF couplerprovided to the RF detector provides an RF signal resulting from RFsignals from at least two RF inputs (e.g., RF signals provided by theantennas), (2) there are a variety of different time delays implementedin transmitting the RF signals from the antennas 120 to the inputs ofthe RF coupler 300.

In the example of FIG. 21, in step S2100, an RF scene in the real worldis sampled by antennas of an antenna array. The RF scene may comprise RFradiation (electromagnetic waves) having a variety of frequencies andangle of arrivals with respect to an antenna array. The RF scene may begenerated by a variety of sources, such as naturally generated RF,manmade generated RF from the RF source, or reflected RF (whether theoriginal RF is generated from a manmade RF source or from a naturallyoccurring RF source). Each antenna 120 of the antenna array converts thedetected RF radiation to a corresponding RF electrical signal.

In step S2110, each of the RF signals output by the antennas areoptionally amplified prior to transmission to an RF coupler.

In steps S2120 and S2130, each of the RF signals are transmitted (S2120)to an RF coupler (such as RF couplers 300 described herein) via RFwaveguides (e.g., coaxial cables), where individual paths of the RFsignal transmission have a variety of different lengths (S2130). Forexample, each RF signal may be transmitted to the RF coupler via acorresponding coaxial cable, where the coaxial cables have a variety ofdifferent lengths. During transmission of the RF signals to the RFcoupler, interference between the transmitted RF signals may be avoidedor otherwise limited (e.g., by electromagnetic shielding), but incertain implementations interference between the transmitted RF signalsmay occur during this transmission. Although some of the path lengthsmay be substantially the same, many (e.g., a majority) of these pathlengths may have substantially different path lengths. The path lengthsof the RF signal transmissions may differ by multiples of the RFwavelength of the RF signals being transmitted. A maximum path-lengthdifference may relate to the spectral resolution of the system. Thedifferent path lengths yield different signal delays between theircapture at the antenna array 110 and the detection by detectors 190 a.The spectral resolution may be generally proportional to the reciprocalof this maximum delay difference.

In step S2140, the transmitted RF signals interfere with one another inthe RF coupler, such as by removing electrical shielding that waspreviously provided by the waveguides (e.g., coaxial cables) thattransmitted the RF signals to the RF coupler. When interference isprovided by an RF coupler, the RF coupler may receive as inputs theplurality of RF signals transmitted via different path lengths from theantenna array 120. The RF coupler may provide an RF interference patternat its output comprising a plurality of individual output RF signals.Each output RF signal output from the RF coupler may include RF signalcomponents from at least two RF signals input to the RF coupler (andthus from RF signals provided by at least two antennas). Thus,correlations may be made between the various received RF signals,including cross-correlation between signals captured by differentantennas 120 of the array 110, and auto-correlation of a signal with itsown delayed version. Further, spectral resolution may be obtained byperforming cross-correlations of the received RF signals with respect todifferent times of when they were received by the antenna array 110.

The number of outputs of the RF coupler need not be the same as thenumber of inputs of the RF coupler. In some implementations, the numberof RF signals output from the RF coupler (such as those describedherein) may exceed the number of RF signals input to the RF coupler. Tobetter utilize the information provided by the input RF signals, thenumber of outputs may be at least [m*(m−1)]/2 and more preferably atleast m*(m−1), where m is the number of inputs.

In step S2150, the resultant interference pattern provided by theplurality of outputs of the RF coupler is recorded. For example, each ofthe individual output RF signals output from the RF coupler is detectedby a corresponding RF detector, such as by measuring (detecting) the RFpower of each output RF signal. As the array of antennas sample theincoming waves spatially, spatial information is maintained in the RFinterference pattern and provides information about the direction ofpropagation of the RF radiation.

In step S2160, the RF sources are reconstructed from the plurality ofdetected RF signals provided by the plurality of RF detectors, resultingin k-space information (direction and frequency (or frequencies)) foreach RF source of the RF scene. Together, the resultant k-spaceinformation of the RF sources may be considered the RF equivalent of avisual image, where pixels forming the image of this RF scene have alocation within the image (as provided by the determined direction, orangle of arrival, of an RF source) and color (frequency—orfrequencies—of an RF source associated with the location).

It will be apparent to those of ordinary skill in the art that theinventive concepts described herein are not limited to the aboveexemplary implementations and the appended drawings and various changesin form and details may be made therein without departing from thespirit and scope of the following claims.

For example, a variety of waveguides may be used other than thosedescribed herein. For example, twisted-pair waveguides (two conductorstwisted in helical fashion around each other) may be used as well, whereinterference between transmitted RF signals may be implemented in aregion where each pair of conductors transmitting an RF signal areuntwisted (e.g., extend in a straight line without twisting around eachany other conductor) (e.g., such as shown in FIG. 19D in the RF coupler300 e, except that rather than using a coaxial cable to transmit RFsignal to the RF coupler, a twisted-pair of conductors is used (onetwisted pair for each RF signal being transmitted and input to the RFcoupler 300 e). Such a modification may be preferable for RF frequenciesless than a few GHz (e.g., less than 3 GHz) where transmission losses ofthe RF signal are minimal or otherwise acceptable.

In addition, structure of the interference module after the RF coupler300 may take several forms. For example, RF detectors 190 a may beintegral with the RF coupler 300 to immediately detect an output RFsignal from the RF coupler 300 without the need to interpose RFwaveguides 140 b between the RF coupler 300 and the RF detectors 190 a.Similarly, location of analog to digital converters 190 b may beimmediately adjacent to the RF couplers 300 or the analog signalsprovided by the RF detectors may be transmitted via appropriateconductive wiring 190 c to the analog to digital converters.

Further, the different lengths of the waveguides should be understood torefer to the total signal path of the RF signal transmitted by thewaveguide, rather than a linear dimension of the waveguide. Thus, acoiled coaxial cable that transmits an RF signal through its tubularlength should be considered to have a length the same as in its uncoiledstate. In general, lengths of the waveguides and/or other variations ofthe transmission paths of the RF signals may act to provide differenttime delays for each of the RF signals from the antennas 120 to the RFcoupler 300.

Although the interference modules have been described herein as beingperformed in the RF domain and/or optical domain, other frequencydomains may also be used to implement the interference module. Inparticular, the interference module may be implemented in the acousticdomain. For example, each of the RF signals detected by the antennas 120of the antenna array may be downconverted by a mixer to an electricalsignal having an acoustic frequency (e.g., between 20 to 20,000 Hz), orultrasonic frequency (e.g. from 20 kHz up to several GHz). Theelectrical signal may be converted to an acoustic signal (e.g., by useof a speaker, or an electro-acoustic transducer) and transmitted alongacoustic paths of different lengths, and allowed to interfere with eachother at an acoustic coupler. Resulting acoustic interference patternmay be detected (e.g., individual signals detected by a plurality ofmicrophones or electro-acoustic transducers) and subsequently processedas discussed above.

What is claimed:
 1. An optical imaging receiver comprising: aphased-array antenna including a plurality of antenna elements arrangedin a first pattern configured to receive RF signals from at least one RFsource; a plurality of electro-optic modulators corresponding to theplurality of antenna elements, each modulator configured to modulate anoptical carrier with a received RF signal to generate a plurality ofmodulated optical signals; a plurality of optical channels configured tocarry the plurality of modulated optical signals and configured to causeinterference amongst the optical signals, each of the plurality ofoptical channels having an output to emanate the corresponding modulatedoptical signal out of the corresponding optical channel, the outputs ofthe plurality of optical channels arranged in a second pattern whichdoes not correspond to the first pattern; a plurality of photodetectorsfor recording the optical signal interference; and a module forcomputationally reconstructing RF sources in k-space from the recordedinterference.